# The degree and radian measure of the angle between the hour-hand and the minute-hand of a clock at tweny minutes past seven is Option 1) $\frac{5\pi }{4}$ Option 2) $\frac{5\pi }{8}$ Option 3) $\frac{5\pi }{7}$ Option 4) $\frac{5\pi^c }{9}$

Sexagesimal System -

In this system, an angle is measured in degrees, minutes and seconds.

- wherein

$1\ right angle = 90^{\circ}$

$1^{\circ} = 60{}'$

$1{}' = 60{}''$

Angle made by hour hand and minute hand is approx $100^{^{\circ}}$ degrees for past seven and two minute total length will be approx 16.6{ because there are 60 gaps and each gap having  $\frac{360}{60}=6$ measurement

$\therefore$ total angle 16.6 X 6 = 99.6 $\simeq 100{}'$

$\frac{5\pi ^{c} }{g}$

[$\because$ the hour hand rotates through an angle of $30^{\circ}$ in one hour or $\left ( \frac{1}{2} \right )^{\circ}$ in one minute.]

Option 1)

$\frac{5\pi }{4}$

This option is incorrect.

Option 2)

$\frac{5\pi }{8}$

This option is incorrect.

Option 3)

$\frac{5\pi }{7}$

This option is incorrect.

Option 4)

$\frac{5\pi^c }{9}$

This option is correct.

Sexagesimal System -

In this system, an angle is measured in degrees, minutes and seconds.

- wherein

$1\ right angle = 90^{\circ}$

$1^{\circ} = 60{}'$

$1{}' = 60{}''$

Angle made by hour hand and minute hand is approx $100^{^{\circ}}$ degrees for past seven and two minute total length will be approx 16.6{ because there are 60 gaps and each gap having  $\frac{360}{60}=6$ measurement

$\therefore$ total angle 16.6 X 6 = 99.6 $\simeq 100{}'$

$\frac{5\pi ^{c} }{g}$

[$\because$ the hour hand rotates through an angle of $30^{\circ}$ in one hour or $\left ( \frac{1}{2} \right )^{\circ}$ in one minute.]

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